The Elder Scrolls V: Skyrim Walkthrough and Strategy Wiki SuperGuide

Smithing

To quickly level your blacksmithing skill, simply craft Iron Daggers over and over. The game doesn't reward more skill experience for a "better" item, and Iron Daggers are by far the cheapest to make, requiring only one Iron Ingot and one Leather Strip. Blacksmith merchants usually carry plenty of these materials, generally anywhere from 10-30 Ingots and 10-20 pieces of leather, and they restock every 24 hours. With a few thousand gold (easily acquired after a few bandit caves), you can quickly level it and have early access to the best armors the game has available (plus a few easy level ups).

The higher your Smithing skill, the better the bonus your weapons and armor will receive when you refine them at a grindstone or workbench. Even if you have already refined your items, if your Smithing skill has increased since then, you can refine it again to make them even stronger. Alchemists will occasionally sell potions that Fortify Smithing skill for a certain amount of time; try to get your hands on one and use it before refining your items, and they will be all the stronger for it (you can also make these potions yourself, if you know the recipe).